| TAMS65 |
Mathematical Statistics, Second Course, 6 ECTS credits.
/Matematisk statistik I, fortsättningskurs/
For:
I
Ii
Mat
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Prel. scheduled
hours: 56
Rec. self-study hours: 104
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
The course is intended to give basic knowledge of the theory and
methods of statistical inference, i.e. how to use observed data to
draw conclusions about phenomena influenced by random factors. By the
end of the course, the student should be able to:
- use an appropriate probability model to describe and analyse observed data and draw conclusions concerning interesting parameters;
- derive point estimators of parameters and analyse their properties;
- understand the principles of statistical inference based on confidence intervals and hypothesis testing;
- construct confidence intervals and test hypotheses using observed
data, draw conclusions and describe the uncertainty;
- explore the nature of the relationships between two or several variables by using simple or multiple linear regression models and discuss the adequacy of the models;
- find probability models and statistical methods in applications from engineering, economy and science and evaluate the results;
- use suitable software (e.g., Matlab, R or similar) for certain types of statistical analyses.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Knowledge of probability, calculus and algebra is assumed and some familiarity with matrix algebra.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Multivariate Statistical Methods, Experimental Design and Biostatistics, Signal Theory, Quality Technology, Six Sigma Quality.
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Organisation:
Teaching is consists of lectures and lessons. Obligatory computer exercises are included in the course.
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Course contents:
Chi-square-, t-, F-distribution. Point estimation, properties of estimators, the method of maximum likelihood, the method of moments and the least squares method. Confidence intervals and tests of hypotheses for one or several samples especially for normal, binomial and Poisson distribution and when the central limit theorem can be applied. Chisquare tests. Random vectors, mean vectors and covariance matrices. The multivariate normal distribution.
Multiple regression, estimation of parameters, confidence intervals, prediction, analysis of variance table, selection of variables and transformations.
Suitable statistical software is used for regression analysis.
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Course literature:
G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst:
Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur.
Grundläggande regressionsanalys (kompendium).
Handbook of formulas and tables published by the department.
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Examination: |
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Written examination
Laboratory work
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5 ECTS
1 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Martin Singull
Link to the course homepage at the department
Course Syllabus in Swedish
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